A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

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3 HUB-LOCATION PROBLEM One of the new topics in location problems is the hub location problem. The first paper on hub location problem was published by Toh and Higgins (1985) and it was on the application of hub location problem in airlines and airports. A comprehensive survey on hub location models and problems can be found in Alumur and Kara 2008. Suppose that there are N nodes and if each node can be either an origin or a destination, then there are N(N-1) origin-destination pairs of nodes in the network. Notice that the pair i-j is different from the j-i pair. Figure 4 shows a network with six nodes (Daskin, 1995). Assume that in this network each vehicle could service five origin-destination pairs every day, and then with six vehicles, six nodes could be serviced every day. hub networks, instead of servicing each spoke directly, hub facilities concentrate flows in order to take advantage of economies of scale. Flows from a spoke are transported to the hub, and are combined with flows that have different origins but the same destination. This fact will reduce the total cost of transportation. In multi hub networks, the hub nodes are completely connected to one another and each spoke is connected to at least one hub such as the network shown in Figure 6 (Hekmatfar and Pishvaee, 2009). Figure 6. Example of a 2-hub network Figure 4. A fully connected network (6 nodes and 30 origin-destination pairs) If one of these nodes is set as a hub node and then connect it to all of the other nodes (which are called spoke), then there will be 2(N-1) connections to service all the spokes via a hub node (Hekmatfar and Pishvaee, 2009). This network is presented in figure 5 and node A is supposed to be the hub node. Figure 5. A hub and spoke network (6 nodes with 6 origin-destination pairs) Again, if each vehicle could service five origin-destination pairs every day, then in this network, with six vehicles, 16 spokes could be serviced every day. Thus, with a fixed transportation capacity, it is possible to service more spokes within a hub network than within a fully connected network. In In multi hub networks the assumption is that, the hubs are connected through low cost and high capacity pathways which causes a discount on the transportation costs between a given hub pair (Naeem, 2009). The advantage of using hubs is the gain of economic profits by establishing more qualitative paths between the hubs. It should be noted that, increasing transportation capacity could decrease transportation costs. On the other hand, increase of transportation capacity is not possible on every path, because traffic of the path will become an important issue in this case. Introducing hub nodes can effectively solve this problem. It means that not only transportation capacity increases, but also there is a low traffic problem as compared to the situation where there is not a hub node. Alumur et. al (2012) studied the hub location problem in the presence of uncertainty about the set-up costs for the hubs and the demands to be transported between the spokes. 4 MATHEMATICAL MODEL OF HUB- LOCATION PROBLEM The hub-location problem involves locating facilities and hub (or hubs) in a 144
23 rd network and allocating spokes to the hub (or hubs). In a hub network, a hub serves every origin-destination pairs with a direct link, and provides service via smaller set of links between the spokes and the hubs. So the objective in a hub location problem is to minimize total cost of transportation (as a function of distance) between hubs, facilities and destination nodes (demands). There are multiple (Fig.6) and single (Fig. 5) versions of hub location problems. In single hub location problems, each destination or demand point must be allocated to be linked to one hub. All flows to and from each demand point travel via the same hub node. In multiple hub-location problems, each demand point could be allocated to be linked to more than one hub. Location of an in pit crusher can be modeled as a single hub location problem. The general form of a single hub problem is as follow ik ij jk ij kj i j k Min f C C y y Subject to : H 1 j j y ij H j 0, i , j H j 0or 1, j y 0or 1, i , j ij In this model f ik is the demand or flow between node i and k, C ij is the unit cost of flow between nodes i and j. if H j is equal to 1, it means to locate a hub at node j. y ij shows that node i is connected to hub located at node j. Equation 1 is the objective function and it minimizes the total cost associated with the transport through the hub. Equation 2 ensures that only one node to be allocated as the hub node. Equation 3 ensures that node i cannot be connected to hub at node j unless we locate the hub at node j. Constraints in 4 and 5 are integrity constraints of the model. The linear form of the objective function in equation 1 can be rewritten as equation 6. This linear form of the problem can now be solved easily. The installing cost of the hub can also be added to the model in order to take account the effect of these cost on overall costs, then the objective function can be rewritten as equation 7. i j k f C C y y ik ij jk ij jk C y f C y f ij ij ik ji ji ki i j k j i k i j C y out in ij ij i i Where out i is the total out flow of node i, and in is the total inflow of node i. i Min C y out in H R i j k ij ij i i k k Where in equation 7, R k is the cost of removing and reinstalling the hub located at node k. In the next section the procedure of selecting the optimal in pit crusher location is prescribed. 5 IN <strong>PIT</strong> CRUSHER LOCATION In this section a method to optimize the location of an in pit crusher (IPC), is introduced. As open pit mines deepens, the haulage distance increases. Deep open pit mines or those open pits with longer haulage distances, require more numbers of trucks (or larger trucks) to produce a constant amount of material. It should be noted that, increasing the numbers of trucks or transportation capacity could decrease costs, but increasing the capacity may not possible on every path. As the transportation capacity increases, the traffic of the path will become an important issue. Introducing an in pit crushing and conveying system as a hub node, can effectively solve the problem. Introducing a hub node, not only increases transportation capacity, but also it lowers the traffic problems. On the other hand, in case of applying an in pit crushing and conveying system, large pits normally require less capital for extending the conveyor system relative to purchasing additional trucks in pure truck-shovel systems. Besides, installing a conveyor system in a long life mining project appears to be more 145
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Chapter - A OPEN PIT MINING
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analisys degradation and erosion ri
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3 METHOLOGICAL APPROACH AND EQUIPME
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Page 135 and 136: 23 rd 6 THE HIERARCHICAL PREFERENC
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A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

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